CHAPTER IX — Critical Commentary & Notes

On Lateral (Prismatic) Columns in Architecture, and on the Quadrature of the Circle.

Historical & Mathematical Commentary

• Aristotle on the Quadrature of the Circle (*Categories* 7b31): Pacioli quotes the classic Scholastic formulation of Aristotle, Categories 7 (7b30–33): Quadratura circuli, si est scibilis, scientia quidem eius nondum est, ipsum vero scibile est (“The squaring of the circle, if it is knowable, is an object of knowledge even though the knowledge of it does not yet exist”). Notice Pacioli’s intriguing hint (“Forse in questo dì è nato chi la darà”, “Perhaps today the man has already been born who will give it”)—likely an allusion to :person:`*Leonardo da Vinci’s <leonardo>`* intense researches on lunules and the quadrature of curved surfaces (De ludo geometrico), which Leonardo was pursuing during their years together!

Philological and Folio Apparatus

• 1509 Paganini Witness Folios: 0075, 0076 (f. 30r–f. 30v)

• Winterberg 1889 Italian Source: winterberg/02_architectura_italian/009_cap_IX.txt

• Winterberg 1889 German Source: winterberg/04_architectura_german/009_cap_IX.txt

• Marginal Woodcut Diagrams: 0 figure(s) extracted from the 1509 Venice witness.